Finite Group Databasebeta

← #29714168

Subgroups — #29714168

Order 15616.

1154 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840458C211yesmaximal, characteristic
2C2×#16840069C211yesmaximal, characteristic, complemented
3C2×#16839860C211yesmaximal, characteristic, complemented
4#21447008C211yesmaximal, characteristic, complemented
5#21447001C211yesmaximal, characteristic, complemented
6#21446820C211yesmaximal, characteristic, complemented
7#21446820C211yesmaximal, characteristic, complemented
8#21446787C211yesmaximal, characteristic, complemented
9#21446618C211yesmaximal, characteristic, complemented
10#21446132C211yesmaximal, characteristic, complemented
11#21446127C211yesmaximal, characteristic, complemented
12#21446016C211yesmaximal, characteristic, complemented
13#21446006C211yesmaximal, characteristic, complemented
14#21445816C211yesmaximal, characteristic, complemented
15C61×#2538C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17#16840458—24no—
18#16840458—24no—
19C2×#14519772—21no—
20C2×#14519769C2211yescharacteristic
21C2×#14519759—21no—
22C2×#14519751C2211yescharacteristic
23C2×#14519751C2211yescharacteristic
24C2×#14519749—21no—
25C2×C4×D244C2211yescharacteristic
26C2×#14519737—21no—
27C2×#14519736C2211yescharacteristic
28C22×C4⋊Dic61C2211yescharacteristic
29#16840069—24no—
30#16839860—24no—
31C2×#14519710C2211yescharacteristic
32C2×#14519710C2211yescharacteristic
33C2×#14519708C2211yescharacteristic
34C2×C4⋊#92418C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43C2×C22⋊#92418C2211yescharacteristic
44C2×C22⋊#92418C2211yescharacteristic
45C2×#14519688C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52C2×C22⋊Q8×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C4×Q8×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C61×#396—21no—
57C61×#396—21no—
58C61×#390—21no—
59C61×#389—21no—
60C61×#384C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#380C2211yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C23×Dic61—21no—
67C22×C4×D61—21no—
68C2×#11758201—22no—
69C2×#11758201—22no—
70C2×#11758201—22no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519772—28no—
76#14519769—22no—
77#14519769D414yes—
78#14519759—28no—
79#14519751—22no—
80#14519751—22no—
81#14519751—22no—
82#14519751—22no—
83#14519749—28no—
84C4×D244—22no—
85C4×D244D414yes—
86#14519737—28no—
87#14519736—22no—
88#14519736—22no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—22no—
91C2×C4⋊Dic61—22no—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×C22⋊Dic61—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×C4×Dic61—21no—
102#14519710—22no—
103#14519710—22no—
104#14519708—22no—
105C4⋊#92418—22no—
106#14519701—22no—
107#14519701—22no—
108#14519701—22no—
109#14519697—22no—
110#14519697—41no—
111#14519697—41no—
112C22⋊#92418—22no—
113C22⋊#92418—22no—
114C22⋊#92418—41no—
115C22⋊#92418—41no—
116#14519688—22no—
117C22×Q8×C61C2311yescharacteristic
118C22×D4×C61D411yescharacteristic
119C23×C4×C61C2311yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C22⋊Q8×C61—22no—
122C22⋊Q8×C61—22no—
123C22⋊Q8×C61—41no—
124C22⋊Q8×C61—41no—
125C4×Q8×C61—22no—
126C4×Q8×C61—22no—
127C4×D4×C61—22no—
128C4×D4×C61—22no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61D411yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61D411yescharacteristic
143C2×C22⋊C4×C61D411yescharacteristic
144C2×C42×C61—21no—
145C2×C42×C61C2311yescharacteristic
146#95×C61—21no—
147#95×C61—21no—
148C24×C61C2×D411yescharacteristic
149C24×C61C2×D411yescharacteristic
150C23×D61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61#4112yes—
157C2×D4×C61—22no—
158C2×D4×C61—22no—
159C2×D4×C61—41no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2411yescharacteristic
181C2×C22⋊D61—24no—
182C2×C22⋊D61—24no—
183C2×C22⋊D61—42no—
184C2×C22⋊D61—42no—
185C2×C22⋊D61—81no—
186C2×C22⋊D61—81no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—24no—
191C22×Dic61—81no—
192C22×Dic61—81no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244C2×D412yes—
199C2×C4×D61—24no—
200C2×C4×D61—81no—
201C2×C4×D61—81no—
202C4⋊C4×C61—22no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—42no—
210C4⋊C4×C61—42no—
211C4⋊C4×C61—42no—
212C4⋊C4×C61—42no—
213C4⋊C4×C61—81no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—22no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61—81no—
219C22⋊C4×C61—81no—
220C42×C61—42no—
221C42×C61C2×D412yes—
222C42×C61C2×D412yes—
223C22⋊Dic61—24no—
224#11758201—28no—
225#11758198—24no—
226#11758198—24no—
227#11758198—24no—
228C4⋊Dic61—24no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61C2×D412yes—
233C4⋊Dic61C2×D412yes—
234C4⋊Dic61C2×D412yes—
235#11758196—24no—
236#11758196—24no—
237C4×Dic61—24no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418#4112yes—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61#13712yes—
264C23×C61C22×D411yescharacteristic
265C22×D61—22no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272Q8×C61—22no—
273Q8×C61—22no—
274Q8×C61—41no—
275Q8×C61—41no—
276D4×C61—44no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—22no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61#12012yes—
308C2×C4×C61#12012yes—
309C2×C4×C61C22×D411yescharacteristic
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C2×#4111yescharacteristic
312C2×C4×C61C2×#4111yescharacteristic
313C2×C4×C61H(5,𝔽2)11yescharacteristic
314C2×C4×C612−1+411yescharacteristic
315C22⋊D61—48no—
316C22⋊D61—84no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—84no—
327D244—22no—
328D244—22no—
329D244—41no—
330D244—41no—
331C4×D61—84no—
332#92418—22no—
333#92418—41no—
334#92418—41no—
335#92418—41no—
336#24138—611nomaximal, Sylow
337C22×C61—22no—
338C22×C61—22no—
339C22×C61—22no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61C2×#12011yescharacteristic
352C22×C61#54611yescharacteristic
353C22×C61#54711yescharacteristic
354C22×C61C2×#13711yescharacteristic
355C22×C61#57511yescharacteristic
356C22×C61#57611yescharacteristic
357C22×C61#57711yescharacteristic
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—81no—
362C2×D61—81no—
363C2×D61—81no—
364C2×D61—81no—
365C4×C61—22no—
366C4×C61—22no—
367C4×C61—41no—
368C4×C61—41no—
369C4×C61—42no—
370C4×C61—81no—
371C4×C61—81no—
372C4×C61—81no—
373C4×C61#52511yescharacteristic
374C4×C61#53711yescharacteristic
375C4×C61#54811yescharacteristic
376C4×C61#55011yescharacteristic
377Dic61—42no—
378Dic61—42no—
379Dic61—42no—
380C2×#553—611no—
381C2×#479—611no—
382C2×#440—611no—
383#2538D6111yescharacteristic, complemented
384#2034—611no—
385#2033—611no—
386#2000—611no—
387#2000—611no—
388#1992—611no—
389#1955—611no—
390#1873—611no—
391#1872—611no—
392#1854—611no—
393#1852—611no—
394#1802—611no—
395C2×C61—42no—
396C2×C61—81no—
397C2×C61#240711yescharacteristic
398C2×C61#300711yescharacteristic
399C2×C61#301211yescharacteristic
400C2×C61#330911yescharacteristic
401C2×C61#332011yescharacteristic
402C2×C61#334611yescharacteristic
403C2×C61#335011yescharacteristic
404D61—82no—
405C22×SD16—611no—
406#553—1224no—
407#553—1224no—
408C2×#126—1221no—
409C2×#125—611no—
410C2×#123—1221no—
411C2×C22⋊Q8C2×D6111yescharacteristic
412C2×C22⋊Q8C2×D6111yescharacteristic
413C2×#121—611no—
414C2×#121—611no—
415C2×#121—1221no—
416C2×C4×Q8C2×D6111yescharacteristic
417C2×C4×D4—611no—
418C2×C4×D4—1221no—
419C2×C4×D4C2×D6111yescharacteristic
420C2×#117—611no—
421C22×C4⋊C4—611no—
422#479—1224no—
423#440—1224no—
424C2×#107—611no—
425C2×#107—611no—
426C2×#106—611no—
427C2×C4⋊C8—611no—
428C2×#103—611no—
429C2×#103—611no—
430C2×#103—611no—
431C2×#102—611no—
432C2×#102—611no—
433C2×#102—611no—
434C2×C22⋊C8—611no—
435C2×C22⋊C8—611no—
436C2×C22⋊C8—611no—
437C2×C22⋊C8—611no—
438C2×#97—611no—
439#396—21no—
440#396—21no—
441#390—21no—
442#389—21no—
443#384C2×D6111yescharacteristic
444#380C2×D6111yescharacteristic
445#380C2×D6111yescharacteristic
446#340—611no—
447#340—611no—
448#340—611no—
449#340—611no—
450#340—611no—
451#340—611no—
452C61#2413811yescharacteristic, complemented, Sylow
453C22×Q8C22×D6111yescharacteristic
454C22×D4—611no—
455C22×D4—1221no—
456C22×D4—1221no—
457C22×D4C22⋊D6111yescharacteristic
458C23×C4—1221no—
459C23×C4—1221no—
460C23×C4C22×D6111yescharacteristic
461C23×C4C22×D6111yescharacteristic
462C2×SD16—1222no—
463C2×SD16—1222no—
464C2×SD16—1222no—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8—611no—
468C22×C8—611no—
469#126—1228no—
470#125—614no—
471#125—1222no—
472#123—1228no—
473C22⋊Q8—22no—
474C22⋊Q8—22no—
475C22⋊Q8—41no—
476C22⋊Q8—41no—
477#121—1222no—
478#121—1222no—
479#121—1222no—
480#121—1222no—
481#121—1228no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—614no—
487C4×D4—1228no—
488C4×D4—1222no—
489#117—1222no—
490#117—1222no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—1222no—
500C2×C4⋊C4—1222no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4C22⋊D6111yescharacteristic
505C2×C4⋊C4C22×D6111yescharacteristic
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C4⋊C4C22×D6111yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4C22⋊D6111yescharacteristic
517C2×C22⋊C4C22⋊D6111yescharacteristic
518C2×C42—21no—
519C2×C42—1221no—
520C2×C42C22×D6111yescharacteristic
521#107—1222no—
522#107—1222no—
523#106—1222no—
524C4⋊C8—1222no—
525#103—1222no—
526#103—1222no—
527#103—1222no—
528#102—1222no—
529#102—2441no—
530#102—2441no—
531C22⋊C8—1222no—
532C22⋊C8—1222no—
533C22⋊C8—2441no—
534C22⋊C8—2441no—
535#97—1222no—
536#95—21no—
537#95—21no—
538C24—1221no—
539C24C2×C22⋊D6111yescharacteristic
540C24C2×C22⋊D6111yescharacteristic
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8#1175822412yes—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—41no—
550C2×D4—612no—
551C2×D4—1224no—
552C2×D4—1224no—
553C2×D4—1221no—
554C2×D4—1221no—
555C2×D4—1221no—
556C2×D4—1221no—
557C2×D4—1221no—
558C2×D4—4881no—
559C2×D4—4881no—
560C2×D4—2442no—
561C2×D4—2442no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—1224no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1224no—
583C22×C4—4881no—
584C22×C4—4881no—
585C22×C4—4881no—
586C22×C4—4881no—
587C22×C4C2×C22⋊D6111yescharacteristic
588C22×C4C2×C22⋊D6111yescharacteristic
589C22×C4C2×C22⋊D6111yescharacteristic
590C22×C4C2×C22⋊D6111yescharacteristic
591C22×C4C23×D6111yescharacteristic
592SD16—1228no—
593C2×C8—612no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—81no—
617C4⋊C4—612no—
618C4⋊C4—612no—
619C4⋊C4—612no—
620C4⋊C4—1224no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1224no—
625C4⋊C4—1224no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—1224no—
633C22⋊C4—1224no—
634C22⋊C4—1224no—
635C22⋊C4—1224no—
636C42—42no—
637C42—1224no—
638C42D4×D6112yes—
639C42D4×D6112yes—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—1222no—
654C23—2441no—
655C23—2441no—
656C23—2441no—
657C23—2441no—
658C23—2441no—
659C23—2441no—
660C23#1451980812yes—
661C23C22×C22⋊D6111yescharacteristic
662Q8—22no—
663Q8—22no—
664Q8—41no—
665Q8—41no—
666D4—44no—
667D4—1222no—
668D4—1222no—
669D4—4884no—
670D4—2448no—
671D4—2441no—
672D4—2441no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—4884no—
707C2×C4—4884no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4#1451974512yes—
715C2×C4#1451974512yes—
716C2×C4C2×D4×D6111yescharacteristic
717C2×C4C2×D4×D6111yescharacteristic
718C2×C4#41×D6111yescharacteristic
719C2×C4C2×#1175822411yescharacteristic
720C2×C4#1451982211yescharacteristic
721C2×C4#1451982411yescharacteristic
722C8—1222no—
723C8—2441no—
724C8—2441no—
725C8—2441no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—4881no—
741C22—4881no—
742C22—4881no—
743C22—4881no—
744C22—2442no—
745C22—2442no—
746C22—2442no—
747C22C2×#1451974511yescharacteristic
748C22#1684040611yescharacteristic
749C22#1684041111yescharacteristic
750C22C2×#1451980811yescharacteristic
751C22#1684056011yescharacteristic
752C22#1684056511yescharacteristic
753C22#1684057011yescharacteristic
754C4—22no—
755C4—22no—
756C4—41no—
757C4—41no—
758C4—42no—
759C4—81no—
760C4—81no—
761C4—81no—
762C4—2442no—
763C4—2442no—
764C4—2442no—
765C4#1684027211yescharacteristic
766C4#1684034111yescharacteristic
767C4#1684041811yescharacteristic
768C4#1684043011yescharacteristic
769C2—42no—
770C2—81no—
771C2—4882no—
772C2#2144916011yescharacteristic
773C2#2145507711yescharacteristic
774C2#2145512011yescharacteristic
775C2#2145782511yescharacteristic
776C2#2145799011yescharacteristic
777C2#2145829811yescharacteristic
778C2#2145836411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2538C2
socleC23×C61C22×D4
prime radicalC2×#16840458C2
hypercenter#2538D61
hypocenterC61#24138
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2538

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#16840069C2semidirect
3. C2×#16839860C2semidirect
4. #21447008C2semidirect
5. #21447001C2semidirect
6. #21446820C2semidirect
7. #21446820C2semidirect
8. #21446787C2semidirect
9. #21446618C2semidirect
10. #21446132C2semidirect
11. #21446127C2semidirect
12. #21446016C2semidirect
13. #21446006C2semidirect
14. #21445816C2semidirect
15. C61×#2538C2semidirect
383. #2538D61semidirect
452. C61#24138semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168404582
C2×#168400692
C2×#168398602
#214470082
#214470012
#214468202
#214467872
#214466182
#214461322
#214461272
#214460162
#214460062
#214458162
C61×#25382
#2413861